The problem involves a three-phase induction motor and requires the calculation of several parameters. Here's how you can solve it:

a) The current I1 = I’2 can be calculated using the formula for the current in a three-phase system:

I1 = P / (√3 * V * pf)

Where P is the power (50 hp = 37300 W), V is the voltage (240 V), and pf is the power factor. The power factor of an induction motor is typically around 0.8 - 0.9, but since it's not given in the problem, we can't calculate the exact current.

b) The torque (t) can be calculated using the formula:

t = P / (2 * π * n / 60)

Where P is the power and n is the speed (1710 rpm).

c) The starting current (Ist) can be calculated using the formula:

Ist = V / ( √3 * Zst)

Where V is the voltage and Zst is the starting impedance. The starting impedance can be calculated using the given resistances and reactances, but since the motor is delta connected, the phase values should be divided by √3.

d) The starting torque (tst) can be calculated using the formula:

tst = 3 * I2^2 * R2 / (2 * π * n / 60)

Where I2 is the rotor current and R2 is the rotor resistance.

e) The maximum torque (tmax) occurs at the slip at which the rotor resistance equals the rotor reactance. It can be calculated using the formula:

tmax = (3 * V^2) / (2 * π * n * (2 * (R2 + √(R2^2 + (X1 + X2)^2))))

f) The maximum slip (Smax) occurs at the maximum torque and can be calculated using the formula:

Smax = R2 / √(R2^2 + (X1 + X2)^2)

g) The torque-speed characteristic can be sketched as a graph with speed on the x-axis and torque on the y-axis. It starts at the starting torque, increases to the maximum torque at the slip at which the rotor resistance equals the rotor reactance, and then decreases to zero at synchronous speed.

Please note that without the exact values of the power factor and the motor's equivalent circuit parameters, the exact numerical answers can't be calculated.

Question

The problem involves a three-phase induction motor and requires the calculation of several parameters. Here's how you can solve it:

a) The current I1 = I’2 can be calculated using the formula for the current in a three-phase system:

I1 = P / (√3 * V * pf)

Where P is the power (50 hp = 37300 W), V is the voltage (240 V), and pf is the power factor. The power factor of an induction motor is typically around 0.8 - 0.9, but since it's not given in the problem, we can't calculate the exact current.

b) The torque (t) can be calculated using the formula:

t = P / (2 * π * n / 60)

Where P is the power and n is the speed (1710 rpm).

c) The starting current (Ist) can be calculated using the formula:

Ist = V / ( √3 * Zst)

Where V is the voltage and Zst is the starting impedance. The starting impedance can be calculated using the given resistances and reactances, but since the motor is delta connected, the phase values should be divided by √3.

d) The starting torque (tst) can be calculated using the formula:

tst = 3 * I2^2 * R2 / (2 * π * n / 60)

Where I2 is the rotor current and R2 is the rotor resistance.

e) The maximum torque (tmax) occurs at the slip at which the rotor resistance equals the rotor reactance. It can be calculated using the formula:

tmax = (3 * V^2) / (2 * π * n * (2 * (R2 + √(R2^2 + (X1 + X2)^2))))

f) The maximum slip (Smax) occurs at the maximum torque and can be calculated using the formula:

Smax = R2 / √(R2^2 + (X1 + X2)^2)

g) The torque-speed characteristic can be sketched as a graph with speed on the x-axis and torque on the y-axis. It starts at the starting torque, increases to the maximum torque at the slip at which the rotor resistance equals the rotor reactance, and then decreases to zero at synchronous speed.

Please note that without the exact values of the power factor and the motor's equivalent circuit parameters, the exact numerical answers can't be calculated.

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